Velocity of Tire at Bottom
Date: Winter 2013-14
Why, during rolling motion, does the bottom-most point of a tire have a velocity that is zero? If it is zero, how does is move forward?
The phenomenon you are asking about is called rolling without slipping, and it's a difficult one to answer without a picture. Take a look at http://www.youtube.com/watch?v=s1qJrNfOCHs. This is a nice explanation of the way parts of a tire move when the tire is in contact with the ground.
Hope this helps.
Excellent question and good thinking. This problem often confuses students much older than you, even some in University.
The place the tire hits the road must be sitting still as far as the road is concerned. If the tire were going faster or slower than the road it would slip and spin, or skid. That is what happens on a dirt road where the wheels spin if you try to go too fast or the car slides when someone hits the brake too hard and the wheels stop turning.
It is the same thing when you are walking. If your foot has any velocity in relation to the ground, it moves over the ground and you slip or slide.
The reason the car, or you for that matter, move is because you are pushing off that place where your foot sticks to the road, not moving. If you are familiar with ice, or very slippery rain soaked streets, you can run all day on these slippery surfaces and, if your foot never sticks to the surface, you will go nowhere.
I hope this helps.
Robert W. Avakian
Oklahoma State University Institute of Technology
Your feet do almost the same thing when you walk. They don't move while they are in contact with the ground. Then you pick them up and quickly move them forward for the next step. On average, they move at the same speed as the rest of you.
If the bottom of the tire was moving forward while the road was not moving, then the tire would be sliding on the road. This would no longer be rolling. For a car, it would also be very dangerous.
For a rolling motion, the middle of the wheel is what must be moving. Consider a wheel ready to roll. Lift it up by the axle, slightly off the ground. Start it spinning, but not traveling. The top of the wheel moves forward, but the bottom of the wheel moves backward. If you move the wheel very slowly forward, the bottom point will still be moving backward as seen from the ground. If you move the wheel forward very fast, the bottom of the wheel will be moving forward as seen from the ground. There is a speed between for which the bottom point of the wheel moves neither forward nor backward.
Just in front of the contact point, the wheel surface is moving straight down, as seen from the ground. Just behind the contact point, the wheel surface as seen from the ground is moving straight upward. At the contact point, the surface is not moving
Dr. Ken Mellendorf
This can be confusing because the tire touches the pavement, and the pavement is not moving. Think, though, of a point on the outside of a tire, as though you created a white "dot" right at the edge of the tire. Now follow that dot as the car moves forward. When the dot is touching the road, it is not moving forward for a moment in time. As the wheel rolls however, the dot starts move forward, and by the time the dot rolls to the top of the wheel, it is moving faster than the speed of the tire moving forward. The result is that over 1 full rotation of the tire, the dot moves as far as the tire does along the road. In other words, when you look in the direction of the road, any point along outside of the tire may be moving at different speeds, but over one tire rotation they have traveled exactly the distance of the tire circumference. Every point, at some point along the rotation, comes to a stop at the road surface.
Kyle J. Bunch, PhD, PE
It does not. It has rotational velocity around the axle. Do not confuse this with linear motion parallel to the surface of the road. This happens if the brakes are locked and the tire skids along the pavement.
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